Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-5x+y &= -8 \\ 4x-y &= 6\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-x = -2$ Divide both sides by $-1$ and reduce as necessary. $x = 2$ Substitute $2$ for $x$ in the top equation. $-5( 2)+y = -8$ $-10+y = -8$ $y = 2$ $y = 2$ The solution is $\enspace x = 2, \enspace y = 2$.